A general inequality for contact CR-warped product submanifolds in cosymplectic space forms

TL;DR

This paper establishes an optimal geometric inequality for contact CR-warped product submanifolds in cosymplectic space forms, extending Chen's foundational work and providing new inequalities involving curvature and submanifold structure.

Contribution

The paper introduces a new optimal inequality for contact CR-warped product submanifolds in cosymplectic space forms, using Gauss and Codazzi equations, and derives additional inequalities for compact invariant factors.

Findings

Proved an optimal inequality for contact CR-warped product submanifolds.

Derived two geometric inequalities for submanifolds with compact invariant factors.

Extended Chen's study to a broader class of submanifolds in cosymplectic space forms.

Abstract

B.-Y. Chen initiated the study of warped product submanifolds in his fundamental seminal papers \cite{C1,C2,C2.1}. In this paper, we study contact CR-warped product submanifolds of cosymplectic space forms and prove an optimal inequality by using Gauss and Codazzi equations. In addition, we obtain two geometric inequalities for contact CR-warped product submanifolds with a compact invariant factor.